qtl (version 1.66)

fitqtl: Fit a multiple-QTL model

Description

Fits a user-specified multiple-QTL model. If specified, a drop-one-term analysis will be performed.

Usage

fitqtl(cross, pheno.col=1, qtl, covar=NULL, formula, method=c("imp", "hk"),
       model=c("normal", "binary"), dropone=TRUE, get.ests=FALSE,
       run.checks=TRUE, tol=1e-4, maxit=1000, forceXcovar=FALSE)

Value

An object of class fitqtl. It may contains as many as four components:

• result.full is the ANOVA table as a matrix for the full model result. It contains the degree of freedom (df), Sum of squares (SS), mean square (MS), LOD score (LOD), percentage of variance explained (%var) and P value (Pvalue).

• lod is the LOD score from the fit of the full model.

• result.drop is a drop-one-term ANOVA table as a matrix. It contains degrees of freedom (df), Type III sum of squares (Type III SS), LOD score(LOD), percentage of variance explained (%var), F statistics (F value), and P values for chi square (Pvalue(chi2)) and F distribution (Pvalue(F)). Note that the degree of freedom, Type III sum of squares, the LOD score and the percentage of variance explained are the values comparing the full to the sub-model with the term dropped. Also note that for imputation method, the percentage of variance explained, the the F values and the P values are approximations calculated from the LOD score.

• ests contains the estimated QTL effects and standard errors.

When method="normal", residuals are saved as an attribute of the output, named "residuals" and accessible via the

attr function.

The part to get estimated QTL effects is fully working only for the case of autosomes in a backcross, intercross, RIL or doubled haploids. In other cases the values returned are based on a design matrix that is convenient for calculations but not easily interpreted.

Arguments

cross

An object of class cross. See read.cross for details.

pheno.col

Column number in the phenotype matrix which should be used as the phenotype. One may also give a character string matching a phenotype name. Finally, one may give a numeric vector of phenotypes, in which case it must have the length equal to the number of individuals in the cross, and there must be either non-integers or values < 1 or > no. phenotypes; this last case may be useful for studying transformations.

qtl

An object of class qtl, as output from makeqtl.

covar

A matrix or data.frame of covariates. These must be strictly numeric.

formula

An object of class formula indicating the model to be fitted. (It can also be the character string representation of a formula.) QTLs are referred to as Q1, Q2, etc. Covariates are referred to by their names in the data frame covar.

method

Indicates whether to use multiple imputation or Haley-Knott regression.

model

The phenotype model: the usual model or a model for binary traits

dropone

If TRUE, do drop-one-term analysis.

get.ests

If TRUE, return estimated QTL effects and their estimated variance-covariance matrix.

run.checks

If TRUE, check the input formula and check for individuals with missing phenotypes or covariates.

tol

Tolerance for convergence for the binary trait model.

maxit

Maximum number of iterations for fitting the binary trait model.

forceXcovar

If TRUE, force inclusion of X-chr-related covariates (like sex and cross direction).

Author

Hao Wu; Karl W Broman,

Details

The formula is used to specified the model to be fit. In the formula, use Q1, Q2, etc., or q1, q2, etc., to represent the QTLs, and the column names in the covariate data frame to represent the covariates.

We enforce a hierarchical structure on the model formula: if a QTL or covariate is in involved in an interaction, its main effect must also be included.

In the drop-one-term analysis, for a given QTL/covariate model, all submodels will be analyzed. For each term in the input formula, when it is dropped, all higher order terms that contain it will also be dropped. The comparison between the new model and the full (input) model will be output.

The estimated percent variances explained for the QTL are simplify transformations of the conditional LOD scores by the formula \(h^2 = 1 - 10^{-(2/n) {\rm LOD}}\). While these may be reasonable for unlinked, additive QTL, they can be completely wrong in the case of linked QTL, but we don't currently have any alternative.

For model="binary", a logistic regression model is used.

The part to get estimated QTL effects is not complete for the case of the X chromosome and 4-way crosses. The values returned in these cases are based on a design matrix that is convenient for calculations but not easily interpreted.

The estimated QTL effects for a backcross are derived by the coding scheme \(\pm\) 1/2 for AA and AB, so that the additive effect corresponds to the difference between phenotype averages for the two genotypes. For doubled haploids and RIL, the coding scheme is \(\pm\) 1 for AA and BB, so that the additive effect corresponds to half the difference between the phenotype averages for the two homozygotes.

For an intercross, the additive effect is derived from the coding scheme -1/0/+1 for genotypes AA/AB/BB, and so is half the difference between the phenotype averages for the two homozygotes. The dominance deviation is derived from the coding scheme 0/+1/0 for genotypes AA/AB/BB, and so is the difference between the phenotype average for the heterozygotes and the midpoint between the phenotype averages for the two homozygotes.

Epistatic effects and QTL \(\times\) covariate interaction effects are obtained through the products of the corresponding additive/dominant effect columns.

References

Haley, C. S. and Knott, S. A. (1992) A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity 69, 315--324.

Sen, Ś. and Churchill, G. A. (2001) A statistical framework for quantitative trait mapping. Genetics 159, 371--387.

See Also

summary.fitqtl, makeqtl, scanqtl, refineqtl, addtoqtl , dropfromqtl, replaceqtl, reorderqtl

Examples

data(fake.f2)

# take out several QTLs and make QTL object
qc <- c(1, 8, 13)
qp <- c(26, 56, 28)
fake.f2 <- subset(fake.f2, chr=qc)
fake.f2 <- subset(fake.f2, ind=1:50)
fake.f2 <- calc.genoprob(fake.f2, step=2, err=0.001)
qtl <- makeqtl(fake.f2, qc, qp, what="prob")

# fit model with 3 interacting QTLs interacting
# (performing a drop-one-term analysis)
lod <- fitqtl(fake.f2, pheno.col=1, qtl, formula=y~Q1*Q2*Q3, method="hk")
summary(lod)

if (FALSE) {
# fit an additive QTL model
lod.add <- fitqtl(fake.f2, pheno.col=1, qtl, formula=y~Q1+Q2+Q3, method="hk")
summary(lod.add)

# fit the model including sex as an interacting covariate
Sex <- data.frame(Sex=pull.pheno(fake.f2, "sex"))
lod.sex <- fitqtl(fake.f2, pheno.col=1, qtl, formula=y~Q1*Q2*Q3*Sex,
                  cov=Sex, method="hk")
summary(lod.sex)

# fit the same with an additive model
lod.sex.add <- fitqtl(fake.f2, pheno.col=1, qtl, formula=y~Q1+Q2+Q3+Sex,
                      cov=Sex, method="hk")
summary(lod.sex.add)

# residuals
residuals <- attr(lod.sex.add, "residuals")
plot(residuals)
}